1. Field of the Invention
The current invention relates to a method of fabricating a dielectric medium comprising two materials with discrete interfaces between the two and media so formed.
2. Discussion of Prior Art
Electronic band structure is a familiar concept to most physicists and electrical engineers: within a crystalline material the band structure describes the ranges of energies accessible to electrons travelling within the material under the influence of an applied electric field. Of particular interest in such materials is the “electronic band gap”—a range of energies within which propagation through the crystal is forbidden to electrons possessing such energies. The gap arises from destructive interference of the electronic wavefunctions Bragg-reflected from crystal planes formed from the periodic arrangement of constituent atoms or molecules within the crystal. The gap is instrumental in explaining such macroscopic phenomena as thermal and electrical conductivity, and is exploited in the design of semiconductors and hence electronic devices.
Yablonovitch [1] and John [2] suggested that similar principles should apply to the electromagnetic (EM) field propagating through periodic media—that is to say that a spatially periodic distribution of electrical permittivity could give rise to a “photonic band gap”, which is a range of frequencies for which EM propagation is forbidden in any direction within the periodic medium. Such a material is known as a “photonic crystal”. The word “photonic” implies an association with phenomena in the optical and near-infrared regions of the EM spectrum, and, indeed, this was the application region intended by Yablonovitch and others. The principle of the phenomenon, however, extends over the whole EM spectrum and although the specific examples presented herein relate to the microwave region, nothing in this specification should be construed as limiting the scope of the invention to that or any other region.
The face-centred-cubic (FCC) crystal lattice was initially suggested by both Yablonovitch and John as the best structure in which to observe the photonic band gap. It possesses the most nearly spherical Brillouin zone of all the 14 Bravais lattices, and is thus the most likely to possess a full (i.e. extending over all 4π steradians) and absolute (i.e. applying to both EM polarisations) band gap. The complete description of the full crystal structure requires specification of the basis (the content of the unit cell) as a dielectric distribution function in space.
Yablonovitch et al [3] were able to demonstrate the existence of a full and absolute photonic band gap at microwave frequencies. They successfully exhibited the effect in an FCC crystal formed by drilling into a proprietary homogeneous high-permittivity and lossless material—Stycast Hi-K™. This material, manufactured by Emerson and Cuming (now part of W. R. Grace) is a composite comprising a low-permittivity polymer (polystyrene) and a high-permittivity powdered filler (titanium dioxide). It is available commercially in a range of dielectric loading, with permittivities from 3 to 30. Yablonovitch chose a permittivity of 12 (closest to 13.6, the dielectric constant of GaAs at optical frequencies). His structure was fabricated by drilling out three circularly cylindrical voids through each point on a hexagonal arrangement of points on the surface of the polymer. Each cylinder was angled at 34.26° from the vertical, with the three voids arranged at 120° azimuthally from each other. The surface holes were separated by 11 mm and had a radius of 0.5 mm. This drilling process produced a structure in which the cylindrical voids intersected within the material to form an FCC crystal with a single axis of symmetry in the [111] direction. The structure was 78% empty. It is a patented structure [3a] and has been dubbed “Yablonovite” [4a].
Yablonovitch [3] also suggested another structure involving the drilling of a further 3 sets of holes in planes perpendicular to the [111] direction. This latter structure possesses full 6-fold diamond symmetry and has proved impractical to fabricate using drilling methods. It has been predicted to have a broader band gap than the 3-cylinder structure [4b].
The 3-cylinder material has been shown by Yablonovitch [3] to suppress propagation to the level of 9 dB per crystal layer. In the [110] direction a 6-layer crystal exhibited a 50 dB attenuation over a frequency gap in the transmission spectrum over a width of 20% of the centre frequency, 15 GHz. More importantly, when defects in the crystal structure were introduced by breaking internal dielectric bridges, a narrow transmission peak appeared in the centre of the gap [5].
An alternative structure for the fabrication of 3-dimensional photonic crystals is described in refs. 5a, 5b, and 5c. This consists of a layer-by-layer arrangement of spaced dielectric rods, usually of rectangular cross-section. The utility of this system is that the structure can be fabricated by stacking wafers of one-dimensional etched gratings.
Each of these structures is of a very specific type, and is associated with a specific method of fabrication. In fact, there exists an infinity of structures which can, in principle, give rise to the photonic band gap phenomenon. It is possible that one of these structures will possess better physical properties (ie. in terms of width of gap for a given dielectric contrast of constituent materials) than these. It is thus valuable to have a general method of construction of photonic crystal.
The suppression of propagation within the material renders a block of the crystal effectively reflective to all incident radiation within the bandgap, at all angles, with no absorptive loss. It is this property, together with that of selective spectral transmissivity within a stop band, which is of interest in terms of potential application.
The band gap itself can be designed to provide a broad (up to 30% of the centre frequency [4]) blocking filter, and the introduction of symmetry-breaking defects can give rise to a transmission window within the gap. This can be designed to be very narrow with respect to the width of the gap; the result is a narrow-band notch filter.
Another potential application is as a perfectly reflecting substrate for a dipole antenna, for which the photonic crystal acts as an efficient mirror, ensuring that the greater part of the emitted radiation generated is transmitted and not absorbed in the substrate. Early investigations have already demonstrated improved efficiency from such antennas [6]. Further applications are as lossless media for waveguides and cavity oscillators. A large number of further applications for these structures is revealed in ref. 5d.
The current invention employs the use of StereoLithography (SL) rapid prototyping. SL is one of a number of rapid prototyping technologies which can fabricate a large range of three-dimensional objects. The SL apparatus (SLA) can build in a few hours 3-dimensional macroscopic objects according to a computer file produced on a computer-aided design (CAD) workstation system.
The design is performed using proprietary 3-dimensional modelling CAD software. The software package includes a filter to output the CAD file into a .STL file (.STL being a standard suffix for file types used in rapid prototyping). The .STL file is then modified using proprietary software (“Bridgeworks”) to include any support structures needed in the construction of the three-dimensional object. Finally, further proprietary software (“Maestro” supplied by 3D Systems—see below) computes appropriate parameters from the three-dimensional object to drive the SLA machine via an attached PC computer.
